I have a small collection of different size shot glasses. How can I figure out how many ounces each one holds when full?
Fill them with liquid and measure the volume with a volume measure, or weigh them while empty and filled with water, whichever you have the better measuring equipment for.
Make a template of the internal profile, if it’s equal when rotated, find a close function using regression, use integration to find volume.
Get yourself a measuring spoon, and start spooning water into each one. Two Tablespoons is one fluid ounce. When you find one that has a one-ounce capacity, use it to measure ounces into the rest. This will identify the one-ounce shots. Move up one size with another tablespoonful of water to identify your 1.5 oz. shots. If you get larger than that, you’re into the quarter-cup range (which is why I doubt you will).
I suppose I should have opened by determining exactly WHY you want to know the capacities, and whether you’re interested in precise up-to-the-brim values or portion-size values.
Get a digital scale and do it by mass/weight. Put the glass on the scale, tare the scale, fill with water and record the weight in grams (which is equal to the volume in cc). Repeat for each glass.
Don’t bother with measuring volume. It will be tedious, and the surface tension will cause problems: Some water will stick to the glass when you pour it out, and the meniscus will complicate the measurement.
How exact do you need the measure, because the formula for the volume of a truncated cone is:
V = π × h × (R²+r²+R×r) ⁄ 3
I suspect you’ll find discrete numbers of jiggers, which is 1/18[sup]th[/sup] an Imperial fifth (or 1-1/2 ounces).
There are 10[sup]-4[/sup] cubic furlongs per jigger
This is such a trivial task. Is there really any reason to bring algebra into it?
The first sentence in the second post nailed it.
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Fill shot glass with water.
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Pour water into measuring cup.
It has to do with saying Kiddush on Shabbat morning using scotch instead of grape juice. There should be a minimum amount used; I just wanted to make sure I was using the correct amount.
C’mon, I know you were joking, but at least make an effort there. A jigger is actually 5.45*10[sup]-12[/sup] cubic furlongs. 10[sup]-4[/sup] cubic furlongs would fill a decent-sized swimming pool.
THIS
My wife bought a smallish digital kitchen scale (<$20) that I’ve used for a bunch of weird measurements. It avoids mathematical gymnastics and it’s really easy and accurate.
Ouch, my number is a square furlong 3 inches tall … opps … but that is a lot of Scotch …
The tare and weight method is much more precise. If the OP used international units it would be almost instantaneous.
Not precisely, but close enough.
I’d get a dosage syringe from a pharmacy, fill it and add it to the shot glass and keep track of how much your adding.
And if the amount is too small to get a reading from the measuring cup, just pour, for example, 10 shots and then divide the measure by 10.